We explore the long-run demand for M1 based on a dataset comprising 38 countries and relatively long sample periods, extending in some cases to over a century. Overall, we find very strong evidence of a long-run relationship between the ratio of M1 to GDP and a short-term interest rate, in spite of a few failures. The standard log-log specification provides a very good characterization of the data, with the exception of periods featuring very low interest rate values. This is because such a specification implies that, as the short rate tends to zero, real money balances become arbitrarily large, which is rejected by the data. A simple extension imposing limits on the amount that households can borrow results in a truncated log-log specification, which is in line with what we observe in the data. We estimate the interest rate elasticity to be between 0.3 and 0.6, which encompasses the well-known squared-root specification of Baumol and Tobin.

This appendix supports Staff Report 587. An earlier version of this Staff Report circulated as Working Paper 738.

We explore the long-run demand for M1 based on a data set that has comprised 32 countries since 1851. In many cases, cointegration tests identify a long-run equilibrium relationship between either velocity and the short rate or M1, GDP, and the short rate. Evidence is especially strong for the United States and the United Kingdom over the entire period since World War I and for moderate and high-inflation countries. With the exception of high-inflation countries–for which a “log-log” specification is preferred–the data often prefer the specification in the levels of velocity and the short rate originally estimated by Selden (1956) and Latané (1960). This is especially clear for the United States and other low-inflation countries.